The rapid advance of nanotechnology has generated much excitement in the scientific and engineering community. Its application to the biological front created the new area of single-molecule biology: Scientists were able to investigate biological processes on a molecule-by-molecule basis, opening the door to addressing many problems that were inaccessible just a few decades ago. The new frontier also raises many statistical challenges, calling upon an urgent need for new statistical inference tools and new stochastic models because of the stochastic nature of single-molecule experiments and because many classical models derived from oversimplified assumptions are no longer valid for single-molecule experiments. The current proposal focuses on the statistical challenges in the single-molecule approach to biology. The proposed research consists of three projects: (1) Using stochastic networks to model enzymatic reaction kinetics. The goal is to provide models not only biologically meaningful, but also capable of explaining the recent single-molecule experimental discoveries that contradict the classical Michaelis-Menten model. (2) Using the kernel method to infer biochemical properties from doubly stochastic Poisson process data, in particular, photon arrival data from single-molecule experiments. The goal is to develop nonparametric inference tools to recover the dependence structure, such as the autocorrelation function, from the doubly stochastic Poisson data. (3) Using bootstrap moment estimates to infer the helical diffusion of DNA-binding proteins. The goal is to elucidate how DNA-binding proteins interact with DNA, and estimate the associated energy landscape. The proposed research aims to provide essential statistical models and inference tools to study biological processes at the single-molecule level and to advance significantly our understanding of how important biological processes such as enzymatic reactions and protein-DNA interactions actually occur in our cells. The single-molecule approach to biology presents many opportunities for interdisciplinary research, calling upon collective efforts from mathematical, biological and physical scientists. The proposed research seeks to meet a high academic standard and aims to reach out to the general scientific community to collaborate and cross-fertilize the interdisciplinary field.